Aaron Carter's Family Says He Didn't Drown, Believe it Was an Overdose

Aaron Carter was found dead in his bathtub, but his family now says he didn't die from drowning ... instead, they believe drugs killed him.

Aaron's fiancée, Melanie Martin, and mother, Jane Carter, tell TMZ ... the L.A. County Coroner's Office told them there was no water found in Aaron's lungs, which rules out drowning as a potential cause of death.

Melanie and Jane say the coroner is still waiting on toxicology results to determine what was in Aaron's system when he died, and the family wants law enforcement to investigate an alleged drug deal the night of Aaron's death.

TMZ broke the story, cops were called to Aaron's L.A. area home back in November for a report of a drowning.

Law enforcement believes Aaron's body was in the tub for a long time as there was a smell of decomposition and the water had turned an unnatural color.

Plus we're told the tub's jets were still running when Aaron's body was found.

Melanie has Aaron's phone and she says she found text messages with an unidentified person telling Aaron he owed $800 for an unknown substance. She says the conversation includes Aaron telling the person he didn't need the substance anymore, to which the person responded that it didn't matter and he still owed money.

Melanie says Aaron asked the person if he was being threatened, and that's where the conversation ends. She tells us she met with investigators last week, and submitted the exchange for evidence.

The family believes Aaron might have met with the person he was texting before his death ... and they fear Aaron took a substance that could have ultimately killed him.

As we first told you, cops found multiple cans of compressed air in Aaron's bathroom and bedroom, as well as prescription pills.

However, Aaron's family believes his death was NOT caused by huffing compressed air ... and they want police to investigate the possibility someone sold Aaron a substance that caused a fatal overdose.